Tag Archives: math

Online AMC 12/AIME Precalculus Summer (Evening) Course (for Rising 7th to 12th Graders) Starting July 31

Posted on 2024-04-03 | Leave a comment

Summer is the golden time to develop students’ math skills and prepare for the American Math Competitions!

  • How to Prepare for the AMC 12
  • 2024 AMC 8: 10 perfect scorers. 54 students got the DHR. 29 students got the HR.
  • 2023 AMC/AIME: 99 AIME qualifiers. 1 AMC 10 perfect scorer. 1 AMC 12 perfect scorer.
  • 2023 JMO/AMO: 8 USAMO Awardees and 7 USAJMO Awardees
    • 1 USAMO Gold Award, 1 USAMO Silver Award, 4 USAMO Bronze Awards, and 2 USAMO Honorable Mention Awards.
    • 1 USAJMO Top Winner, 1 USAJMO Winner, and 5 USAJMO Honorable Mention Awards.
  • 2023 MOP: 4 MOP winners.

Purpose: To prepare for the 2024 AMC 10/12 and the 2025 AIME contests.

Course Outline
6 Classes (Eastern Time: 6:00 – 9:00 pm), Total: 18 Hours
7/31, 8/2, 8/4, 8/6, 8/8, 8/10 (Mock Exam/Review)

Online Registration is now open! Click HERE to register and pay. 

Tuition (including all materials)
New Student Via Zelle:  $810 (Phone: 240-300-4380)
Please include your child’s name “AMC 12-AIME Precalculus” in the “Memo” box.
Via PayPal:  $840  Buy Now Button
Returning Student Via Zelle:  $790 (Phone: 240-300-4380)
Please include your child’s name “AMC 12-AIME Precalculus” in the “Memo” box.
Via PayPal:  $820  Buy Now Button
Click HERE to see payment and refund policy.
  • This is a live class, not a pre-recorded one. Instructors will ask students questions, and students can also ask questions during the class or email their questions to instructors after class.
  • We record all of our lessons as a big bonus so that our students can watch class videos after class for review and self-study.

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You are very welcome to sign up for our online course which offers a quick, efficient way for students to interact with teachers over long distance. We use Google Meet to video chat and easily connect with students to teach them our tricks and shortcuts to getting an amazing score on their contests, as well as offer them our guidance and support. Students can ask questions face-to-face, and can complete problems with the supervision of our teachers/coaches. Click HERE to see detailed instruction.

A commitment to the whole course can maximize the benefit of learning all the math ideas, methods, strategies, tactics, skills, and techniques.

  • We will focus on efficient tricks, shortcuts, and strategies to solve competitive precalculus problems, especially those hard problems on the AMC 12 and easy problems on the AIME, as well as test-taking tactics.
  • We will utilize a highly effective teaching model as described in the article: Small-sized Class Instruction-focused Model.

Instructors:

Contact Information:
Ivy League Education Center
Tel:  240-300-4380     or     240-406-3402
Email:  chiefmathtutor@gmail.co

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Specific Goal: 

To earn a score of 100 or more out of 150 on the American Mathematics Contest 12 (AMC 12), and then qualify for the American Invitational Mathematics Examination (AIME), which is used to determine qualification for the United States of America Mathematical Olympiad (USAMO).

AMC-General

There are many math competitions in the United States. Of those, only

AMC → AIME → USAMO sequence

would take you to the IMO (International Math Olympiad), the highest level math competition for high school students in the world!

AMC 10-12-New
Click here to read more!

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Who should take this class: This class is very appropriate for raising 6th-12th grade students who are hoping to qualify for the AIME.

Benefits:

  • 6 tutorial handouts (>360 pages) developed by Dr. Henry Wan and 200 new precalculus problems similar to AMC 12 level from the licensed AMC Database
  • One FREE mock test that is intended to mimic an actual math competition exam, each of which has 25 questions similar to AMC 12 level taken from the licensed AMC Database. These simulated tests help students assess their level of preparation for the Math Competitions. After attempting the test, students get answers, explanations, and a detailed score report and wise performance summary.
  • FREE registration for the AMC 10/12A — Wednesday, November 6, 2024 and AMC 10/12B — Tuesday, November 12, 2024. Please see: The AMC 10/12 Online Contests on November 6, 2024, and November 12, 2024

Weekly Homework:

At least 6 hours per week. Problem sets include all problems on the past AMC 10/12 and ARML, and 500 brand new problems having similar difficulty and style as the real AMC 10/12 problems, extracted from the licensed AMC Database.

The focus will on the final 15 problems on the AMC 12, and the first 5 problems on the AIME, as well as those hard problems on the ARML. Note that some hard problems on the recent AMC 10 and 12 are exactly the same as previous ARML Problems.

Read More at:

Each week, we will carefully review and check 2 students’ homework, and correct any mistakes. The next week, we will check another 2 students’ homework, and this will continue on a rotational basis until all students have had their homework checked at least once and the cycle will start again. Based on the work of the 2 students that week, we will provide the those 2 students with individualized proposal and support.

Qualifying AIME
Class Outline:
This class focuses on precalculus topics that are only needed for the AMC 12 and AIME. We will also help students develop quick problem solving strategies and effective time management skills.

Class Date Topic
1 7/31, Wed Exponents and Logarithms
2 8/2, Fri Fundamental Trigonometry
3 8/4, Sun Advanced Trigonometry
4 8/6, Tue Complex Numbers
5 8/8, Thur Conic Sections: Parabolas, Circles, Ellipses, and Hyperbolas
6 8/10, Sat Three-dimensional Coordinate Geometry
We reserve the right to adjust the teaching content and method according to students’ understanding and comprehension of new knowledge.

AMC Logo

Small-sized Class Teaching Model:

We utilize the highly effective small-sized class teaching model. Smaller classes lead to pupils receiving more individual attention from teachers, and having more active interactions with them. We focus on every individual, not the whole class. Students will thrive from the smaller class sizes that allow them to reach their full potential. Particularly, students can benefit tremendously from high-frequent individualized student-teacher interactions leading to establishment of a stronger foundation for lifelong learning.

Our main purpose is to help our students gain deeper understanding of the fundamental math concepts, build a solid foundation in math, and develop the critical thinking and problem-solving skills that are so valuable to success in any career. We are big believers in the FUNDAMENTALS! Our students will receive the LIFELONG BENEFITS from learning math.

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Regardless of his/her math level, each student will have the opportunity to learn math in a fun, friendly, cooperative, supportive learning environment. The most important thing is to have fun.

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Our Students

In 2024, we had 90 students who obtained top scores on the AMC 8 contest!

  • 10 of our students were among the top 116 worldwide winners (Perfect Scorers).
  • 54 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers. They were among the 697 worldwide winners.
  • 29 students received National Honor Roll Certificates awarded to top 5% test takers. They were among the 2,683 worldwide winners.
  • 93 out of our 96 students (96.9%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2024 AMC 8 Results Just Announced — Ten Students Received Perfect Scores 

In 2023, we had 99 students who qualified for the AIME either through the AMC 10A/12A or the AMC 10B/12B. One of our students was among the 11 Perfect Scorers worldwide on the AMC 10B: Ali R. and one of our students was among the 13 Perfect Scorers worldwide on the AMC 12B: Yaoyun X.  Read more at: 99 Students Qualified for the 2024 AIME and 2 Students Received Perfect Scores on the 2023 AMC 10/12

In 2023, we had 8 students who won USAMO awards and 7 students who won USAJMO awards.

  • 1 USAMO Gold Award, 1 USAMO Silver Award, 4 USAMO Bronze Awards, and 2 USAMO Honorable Mention Awards.
  • 1 USAJMO Top Winner, 1 USAJMO Winner, and 5 USAJMO Honorable Mention Awards.

Read more at: 2023 USAMO and USAJMO Awardees Announced — Congratulations to Eight USAMO Awardees and Seven USAJMO Awardees

In 2023, we had 90 students who obtained top scores on the AMC 8 contest!

  • 8 of our students were among the top 81 worldwide winners (Perfect Scorers).
  • 51 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers. They were among the 697 worldwide winners.
  • 31 students received National Honor Roll Certificates awarded to top 5% test takers. They were among the 2,571 worldwide winners.
  • 90 out of our 93 students (96.8%) received National Awards for the AMC 8 from the Mathematical Association of America.

Read more at: 2023 AMC 8 Results Just Announced — Eight Students Received Perfect Scores

In 2022, we had 96 students who qualified for the AIME either through the AMC 10A/12A or the AMC 10B/12B. One of our students was among the 6 Perfect Scorers worldwide on the AMC 10A: Justin W. and one of our students was among the 3 Perfect Scorers worldwide on the AMC 12B: Ming Y. Read more at: 96 Students Qualified for the 2023 AIME and 2 Students Received Perfect Scores on the 2023 Fall AMC 10/12

In 2022, we had 3 students qualified for the Math Olympiad Summer Program. Read more at: Brendon J., Kyle S., and Isabella Z. Qualified for the 2022 Math Olympiad Summer Program

In 2022, we had 1 student Competes in International Girls’ Math Olympiad. Read more at: sabella Z. Competes in International Girls’ Math Olympiad

In 2022, we had 7 students qualified for the USAMO and 7 students for the USAJMO. Read more at: 2022 USAMO and USAJMO Qualifiers Announced — Seven Students Qualified for the USAMO and Seven Students for the USAJMO.

In 2022, we had 88 students who obtained top scores on the AMC 8 contest!

  • 10 of our students were among the top 131 worldwide winners (Perfect Scorers), as shown in Table 1. Click Here see a full list of the 131 worldwide winners.
  • 52 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers. They were among the 1,010 worldwide winners. Click HERE see a full list.
  • 26 students received National Honor Roll Certificates awarded to top 5% test takers. They were among the 2,449 worldwide winners. Click HERE see a full list.
  • 88 out of our 91 students (96.7%)received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2022 AMC 8 Results Just Announced — Ten Students Received Perfect Scores

In Fall 2021, we had 93 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 5 Perfect Scorers worldwide on the AMC 10A: Nina L. and one of our students was among the 2 Perfect Scorers worldwide on the AMC 10B: Ming Y. Read more at: 93 Students Qualified for the 2021 Fall AIME and 2 Students Received Perfect Scores on the 2021 Fall AMC 10/12

In 2021, we had 6 students qualified for the USAMO and 6 students for the USAJMO. Read more at: 2021 USAMO and USAJMO Qualifiers Announced — Six Students Qualified for the USAMO and Six Students for the USAJMO

In Spring 2021, we had 91 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students was among the 17 Perfect Scorers worldwide on the AMC 12A: Evan L. and Suraj O. and one of our students was among the 27 Perfect Scorers worldwide on the AMC 10A: Xinchen L. Read more at: 91 Students Qualified for the 2021 AIME and 3 Students Received Perfect Scores on the 2021 AMC 10/12

In 2021, we had 8 students who got into the MathCounts state-level top 10. Yunyi L. won 9th Place in the 2021 MathCounts National Competition!

In 2020, we had 79 students who obtained top scores on the AMC 8 contest!

  • 5 of our students were among the top 57 worldwide winners (Perfect Scorers).
  • 49 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 25 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 79 out of our 81 students (97.5%) received National Awards for the AMC 8 from the Mathematical Association of America.

Read more at: 2020 AMC 8 Results Just Announced — Five Students Received Perfect Scores

In 2020, we had 82 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 11 Perfect Scorers worldwide on the AMC 12A: Yiyang X, and one of our students was among the 13 Perfect Scorers worldwide on the AMC 10A: Jason W.. 43 middle schoolers and 9 elementary schoolers qualified for the AIME! Read more at: 2020 AIME Qualifiers Announced — 82 Students Qualified for the AIME

In 2019, we had 71 students who obtained top scores on the AMC 8 contest!

  • 8 of our students were among the top 151 National Winners (Perfect Scorers), including 2 sixth graders.
  • 36 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 27 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 71 out of our 73 students (97.3%) received National Awards for the AMC 8 from the Mathematical Association of America.

Read more at: 2019 AMC 8 Results Just Announced — Eight Students Received Perfect Scores

In 2019, we had 4 Students Qualified for the USAMO and 4 Students for the USJMO.

  • Of the 280 USA Math Olympiad national qualifiers, 4 are our students: Luke C., Zipeng L., Sameer P., and Peter P.
  • Of the 235 USA Junior Math Olympiad national qualifiers, 4 are our students: Michael H., Noah W., Holden W., and Isabella Z.

Read more at: 2019 USAMO and USAJMO Qualifiers Announced — Four Students Qualified for the USAMO and Four Students for the USAJMO

In 2019, we had 76 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 22 Perfect Scorers worldwide on the AMC 10A: Noah W. and one of our students were among the 10 Perfect Scorers worldwide on the AMC 12B: Kenneth W. Very impressively, 32 middle schoolers and 7 elementary schoolers qualified for the AIME!

In 2018, we had 64 students who obtained top scores on the AMC 8 contest!

  • 3 of our students were among the top 44 National Winners (Perfect Scorers): Eric B., Kevin Y., and Isabella Z.
  • 40 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 21 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 64 out of our 66 students (96.5%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2018 AMC 8 Results Just Announced — Three Students Received Perfect Scores

In 2018, we had 73 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students were among the 35 Perfect Scorers worldwide on the AMC 10A: Austen M. and Jason W.  and two of our students were among the 21 Perfect Scorers worldwide on the AMC 12B: Kaan D. and Edward W. Remarkably, 11 middle schoolers and 2 elementary schoolers qualified for the AIME!

In 2017, we had 63 students who earned top scores on the AMC 8 contest!

  • 7 of our students were among the top 75 National Winners (Perfect Scorers).
  • 34 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 22 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 63 out of our 65 students (97%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2017 AMC 8 Results Just Announced — Seven Students Received Perfect Scores

In 2017, we had 61 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 28 Perfect Scorers worldwide on the AMC 10A: Austen M., and two of our students were among the 65 Perfect Scorers worldwide on the AMC 10B: Ashwin A. and Brad Z. Remarkably, eight middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Very impressively, Bryan Z., a 6th grader, gained a score of 132 out of 150 on the AMC 10B.Read more at: 2017 AIME Qualifiers Announced — 61 Students Qualified for the AIME

In 2016, we had 36 students who are qualified to take AIME either through AMC 10A/12A or AMC 10B/12B. One of our students was among the 23 Perfect Scorers worldwide on the AMC 10A: Joel (Junyao) T. Particularly, seven middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Pravalika P., a 6th grader, got a 115.5 out of 150 on the AMC10B, which is very impressive. Read more at: 2016 AIME Qualifiers Announced — 36 Students Qualified for AIME

2011 – 2015: In total, 37 students scored above 120 on the American Mathematics Contest 10 (AMC 10) and qualified for the American Invitational Mathematics Examination (AIME); 26 students scored above 100 on the American Mathematics Contest 12 (AMC 12) and qualified for the American Invitational Mathematics Examination (AIME); 3 students qualified for the USA Mathematical Olympiad (USAMO), the highest level of math competition for high school students in the USA

2011 – 2015: In total, 23 students achieved perfect scores of 28 on the AMC 8

Read more at: Notable Achievements of Our Students

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Our Uniqueness

We have a long history of close collaboration with the MAA’s American Mathematics Competitions (AMC), which are dedicated to strengthening the mathematical capabilities of our nation’s youth, and are the first of a series of competitions in high school mathematics that determine the United States team for the International Mathematical Olympiad (IMO).

We are only one in the Washington DC metropolitan area to offer elementary, middle, and high-school level competition math courses. Our students have received top scores and awards at prestigious national and math competitions.

Great Benefits of Math Competitions

In an increasingly competitive college application pool, the process of mastering math skills through our courses and participating in the American Math Competitions will help students strengthen and diversify their extracurricular activities. These contests can motivate students’ interest and passion in math, and they can discover their talent through solving challenging problems different from those in the school classes. Many top colleges also request AMC scores as part of the college application process. Both MIT and Caltech have entry blanks on their official admission application forms for the applicant to enter their best AMC and AIME scores. Ivy League Colleges and Stanford ask for to the AMC and AIME scores in their Supplement to the Common Application Forms. Your children deserve the chance to list these scores on their applications! Good AMC scores will greatly enhance admission opportunities for students to elite colleges.

Read more at::

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Click HERE find out more about Math Competitions!sat-logo-3

Click HERE to find out more about SAT Prep!

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education priceless treasure

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Online Mental Math (Summer Session) Starting August 3

Posted on 2024-04-01 | Leave a comment
  • 2024 AMC 8: 10 perfect scorers. 54 students got the DHR. 29 students got the HR.
  • 2023 AMC/AIME: 99 AIME qualifiers. 1 AMC 10 perfect scorer. 1 AMC 12 perfect scorer.
  • 2023 JMO/AMO: 8 USAMO Awardees and 7 USAJMO Awardees
    • 1 USAMO Gold Award, 1 USAMO Silver Award, 4 USAMO Bronze Awards, and 2 USAMO Honorable Mention Awards.
    • 1 USAJMO Top Winner, 1 USAJMO Winner, and 5 USAJMO Honorable Mention Awards.
  • 2023 MOP: 4 MOP winners.

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Grade Levels:  Grades 4-11

4 Classes (Eastern Time: 1:00 – 4:00 pm), Total: 12 Hours
8/3, 8/4, 8/10, 8/11 (Mock Exam/Review)

Course Outline

Online Registration is now open! Click HERE to register and pay.

Tuition (including all materials)
Summer Session (12 Hours)
New Student: Via Zelle:  $540 (Phone: 240-300-4380)
Please include your child’s name “Mental Math Summer” in the “Memo” box.
Via PayPal:  $560 Buy Now Button
Returning Student: Via Zelle:  $530 (Phone: 240-300-4380)
Please include your child’s name “Mental Math Summer” in the “Memo” box.
Via PayPal:  $550 Buy Now Button
Click HERE to see payment and refund policy.
  • This is a live class, not a pre-recorded one. Instructors will ask students questions, and students can also ask questions during the class or email their questions to instructors after class.
  • We record all of our lessons as a big bonus so that our students can watch class videos after class for review and self-study.

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Description:

We will reveal powerful mental math techniques that allow you to perform calculations in your head quickly and effortlessly. You will learn to compute faster than you ever imagined, and with practice, your ability to retain and manipulate numbers will improve significantly. These techniques will not only enhance your mathematical skills but also enable you to perform impressive mental feats that will amaze your friends, colleagues, and teachers. Most importantly, you will discover that math can be fun, engaging, and deeply rewarding.

Too often, math is taught as a set of rigid rules, leaving little room for creativity and exploration. However, as you will see in this course, many problems can be solved in multiple ways. By breaking down complex problems into smaller, more manageable parts, we can simplify calculations and uncover clever shortcuts. We also learn to spot patterns and special features that make problem-solving more efficient. These strategies are not just valuable for mathematics — they serve as critical thinking skills that can be applied to problem-solving in everyday life.

One often-overlooked benefit of mental math is that it sharpens your ability to think quickly and make rapid decisions. Based on our years of teaching experience, we have found that speed and accuracy in mental calculations are essential skills that anyone can develop with proper practice. Like any worthwhile ability, mastering mental math requires dedication and strategic practice — but with the right approach, you can achieve remarkable results.

For students competing in mathematics competitions, slow calculation speed and low accuracy are among the biggest obstacles to success. Our program is designed to equip students with effective problem-solving strategies, boost computational speed, and enhance accuracy, ensuring they are well-prepared to excel in competitive mathematics.

Two Typical Mental Math Problems

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You are very welcome to sign up for our online course which offers a quick, efficient way for students to interact with teachers over long distance. We use the Google Meet to video chat and easily connect with students to teach them our tricks and shortcuts to getting an amazing score on their contests, as well as offer them our guidance and support. Students can ask questions face-to-face via Google meet, and can complete problems with the supervision of our teachers/coaches. Click HERE to see detailed instruction.

A commitment to the whole course can maximize the benefit of learning all the mental math ideas, methods, strategies, tactics, skills, and techniques. Click HERE to see attendance/absence/aancellation/makeup lesson policy

  • The emphasis of this class will be on comprehensive problem-solving in mental math. Particularly, we will help students use mental math for accurately and quickly solving math questions in their heads. 
  • We will utilize a highly effective teaching model as described in the article: Small-sized Class Instruction-focused Model.

Instructors: Dr. Henry Wan

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Contact Information:
Ivy League Education Center
Tel:  240-300-4380
Email:  chiefmathtutor@gmail.com

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Class Outline:

This class teaches students to develop quick problem-solving tips, tricks, tactics, and strategies, and improve computational speed and accuracy when preparing for math competitions. In particular, we will help students use mental math for accurately and quickly solving contest questions in their heads. 

We reserve the right to adjust the teaching content and pace according to the actual performance of students .

Class Date Topic
1 8/3, Sat Two Important Tricks for Special Multiplication and Quick Tricks for Fractions, Decimals, and Percents
2 8/4, Sun

Using Difference of Squares to Mentally Square Numbers and Multiply Numbers
3 8/10, Sat

Quick Tricks for Pythagorean Triples, Perfect Squares, Exponents, and Powers
4 8/11, Sun

Quick Tricks for Rationalizing the Denominator and Simplifying Radicals

Two Typical Mental Math Problems:

  • Find the prime factorization of 2024 within few seconds.
  • Find the square of 135 within few seconds.

Speed-Math-BannerHomework:

On average, at least 2 hours per week, as described in the article: Homework assignments are a fundamental part of our courses. Click HERE to see a typical homework sample we developed. Each week, we will carefully review and check 3 students’ homework, and correct any mistakes. The next week, we will check another 3 students’ homework, and this will continue on a rotational basis until all students have had their homework checked at least once and the cycle will start again. Based on the work of the 3 students that week, we will provide the those 3 students with individualized proposal and support. More details can be found in the article: Homework Correction is very Important — We Give an Extensive Correction of the Incorrect Answers of All Homework.do-math

We have to face the simple truth that to do well on these grueling contests, we will need to practice. Just like it is for sports and music, the key to success is repetition and practice. We strongly believe in effort and the malleability of intelligence. Intelligence can be enhanced through effort. People can develop impressive levels of expertise through hard work and practice. Effort and persistence are the keys to success. Hard work always pays off: practice makes perfect!

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Main Purpose:

Our main purpose is to help our students gain deeper understanding of the fundamental mental math concepts, build a solid foundation in mental math, and develop the critical thinking and problem-solving skills that are so valuable to success in any career. We are big believers in the FUNDAMENTALS! Our students will receive the LIFELONG BENEFITS from learning mental math.

Regardless of his/her math level, each student will have the opportunity to learn mental math in a fun, friendly, cooperative, supportive learning environment. The most important thing is to have fun.

Bronze_medal

Our Students

In 2024, we had 90 students who obtained top scores on the AMC 8 contest!

  • 10 of our students were among the top 116 worldwide winners (Perfect Scorers).
  • 54 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers. They were among the 697 worldwide winners. 
  • 29 students received National Honor Roll Certificates awarded to top 5% test takers. They were among the 2,683 worldwide winners. 
  • 93 out of our 96 students (96.9%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2024 AMC 8 Results Just Announced — Ten Students Received Perfect Scores 

In 2023, we had 99 students who qualified for the AIME either through the AMC 10A/12A or the AMC 10B/12B. One of our students was among the 11 Perfect Scorers worldwide on the AMC 10B: Ali R. and one of our students was among the 13 Perfect Scorers worldwide on the AMC 12B: Yaoyun X.  Read more at: 99 Students Qualified for the 2024 AIME and 2 Students Received Perfect Scores on the 2023 AMC 10/12

In 2023, we had 8 students who won USAMO awards and 7 students who won USAJMO awards.

  • 1 USAMO Gold Award, 1 USAMO Silver Award, 4 USAMO Bronze Awards, and 2 USAMO Honorable Mention Awards.
  • 1 USAJMO Top Winner, 1 USAJMO Winner, and 5 USAJMO Honorable Mention Awards.

Read more at: 2023 USAMO and USAJMO Awardees Announced — Congratulations to Eight USAMO Awardees and Seven USAJMO Awardees

In 2023, we had 90 students who obtained top scores on the AMC 8 contest!

  • 8 of our students were among the top 81 worldwide winners (Perfect Scorers).
  • 51 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers. They were among the 697 worldwide winners. 
  • 31 students received National Honor Roll Certificates awarded to top 5% test takers. They were among the 2,571 worldwide winners. 
  • 90 out of our 93 students (96.8%) received National Awards for the AMC 8 from the Mathematical Association of America.

Read more at: 2023 AMC 8 Results Just Announced — Eight Students Received Perfect Scores

In 2022, we had 96 students who qualified for the AIME either through the AMC 10A/12A or the AMC 10B/12B. One of our students was among the 6 Perfect Scorers worldwide on the AMC 10A: Justin W. and one of our students was among the 3 Perfect Scorers worldwide on the AMC 12B: Ming Y. Read more at: 96 Students Qualified for the 2023 AIME and 2 Students Received Perfect Scores on the 2023 Fall AMC 10/12

In 2022, we had 3 students qualified for the Math Olympiad Summer Program. Read more at: Brendon J., Kyle S., and Isabella Z. Qualified for the 2022 Math Olympiad Summer Program

In 2022, we had 1 student Competes in International Girls’ Math Olympiad. Read more at: sabella Z. Competes in International Girls’ Math Olympiad

In 2022, we had 7 students qualified for the USAMO and 7 students for the USAJMO. Read more at: 2022 USAMO and USAJMO Qualifiers Announced — Seven Students Qualified for the USAMO and Seven Students for the USAJMO.

In 2022, we had 88 students who obtained top scores on the AMC 8 contest!

  • 10 of our students were among the top 131 worldwide winners (Perfect Scorers), as shown in Table 1. Click Here see a full list of the 131 worldwide winners.
  • 52 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers. They were among the 1,010 worldwide winners. Click HERE see a full list.
  • 26 students received National Honor Roll Certificates awarded to top 5% test takers. They were among the 2,449 worldwide winners. Click HERE see a full list.
  • 88 out of our 91 students (96.7%)received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2022 AMC 8 Results Just Announced — Ten Students Received Perfect Scores

In Fall 2021, we had 93 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 5 Perfect Scorers worldwide on the AMC 10A: Nina L. and one of our students was among the 2 Perfect Scorers worldwide on the AMC 10B: Ming Y. Read more at: 93 Students Qualified for the 2021 Fall AIME and 2 Students Received Perfect Scores on the 2021 Fall AMC 10/12

In 2021, we had 6 students qualified for the USAMO and 6 students for the USAJMO. Read more at: 2021 USAMO and USAJMO Qualifiers Announced — Six Students Qualified for the USAMO and Six Students for the USAJMO

In Spring 2021, we had 91 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students was among the 17 Perfect Scorers worldwide on the AMC 12A: Evan L. and Suraj O. and one of our students was among the 27 Perfect Scorers worldwide on the AMC 10A: Xinchen L. Read more at: 91 Students Qualified for the 2021 AIME and 3 Students Received Perfect Scores on the 2021 AMC 10/12

In 2021, we had 6 students qualified for the USAMO and 6 students for the USAJMO. Read more at: 2021 USAMO and USAJMO Qualifiers Announced — Six Students Qualified for the USAMO and Six Students for the USAJMO

In 2021, we had 8 students who got into the MathCounts state-level top 10. Yunyi L. won 9th Place in the 2021 MathCounts National Competition!

In 2020, we had 79 students who obtained top scores on the AMC 8 contest!

  • 5 of our students were among the top 57 worldwide winners (Perfect Scorers).
  • 49 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 25 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 79 out of our 81 students (97.5%) received National Awards for the AMC 8 from the Mathematical Association of America.

Read more at: 2020 AMC 8 Results Just Announced — Five Students Received Perfect Scores

In 2020, we had 82 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 11 Perfect Scorers worldwide on the AMC 12A: Yiyang X, and one of our students was among the 13 Perfect Scorers worldwide on the AMC 10A: Jason W.. 43 middle schoolers and 9 elementary schoolers qualified for the AIME!

In 2019, we had 71 students who obtained top scores on the AMC 8 contest!

  • 8 of our students were among the top 151 National Winners (Perfect Scorers), including 2 sixth graders.
  • 36 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers, as shown in Table 2.
  • 27 students received National Honor Roll Certificates awarded to top 5% test takers, as shown in Table 3.
  • 71 out of our 73 students (97.3%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2019 AMC 8 Results Just Announced — Eight Students Received Perfect Scores

In 2019, we had 4 Students Qualified for the USAMO and 4 Students for the USJMO.

  • Of the 280 USA Math Olympiad national qualifiers, 4 are our students: Luke C., Zipeng L., Sameer P., and Peter P.
  • Of the 235 USA Junior Math Olympiad national qualifiers, 4 are our students: Michael H., Noah W., Holden W., and Isabella Z.

Read more at: 2019 USAMO and USAJMO Qualifiers Announced — Four Students Qualified for the USAMO and Four Students for the USAJMO

In 2019, we had 76 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 22 Perfect Scorers worldwide on the AMC 10A: Noah W. and one of our students were among the 10 Perfect Scorers worldwide on the AMC 12B: Kenneth W. Very impressively, 32 middle schoolers and 7 elementary schoolers qualified for the AIME!

In 2018, we had 64 students who obtained top scores on the AMC 8 contest!

  • 3 of our students were among the top 44 National Winners (Perfect Scorers): Eric B., Kevin Y., and Isabella Z.
  • 40 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 21 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 64 out of our 66 students (96.5%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2018 AMC 8 Results Just Announced — Three Students Received Perfect Scores

In 2018, we had 73 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students were among the 35 Perfect Scorers worldwide on the AMC 10A: Austen M. and Jason W.  and two of our students were among the 21 Perfect Scorers worldwide on the AMC 12B: Kaan D. and Edward W. Remarkably, 11 middle schoolers and 2 elementary schoolers qualified for the AIME!

In 2017, we had 63 students who earned top scores on the AMC 8 contest!

  • 7 of our students were among the top 75 National Winners (Perfect Scorers).
  • 34 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 22 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 63 out of our 65 students (97%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2017 AMC 8 Results Just Announced — Seven Students Received Perfect Scores

In 2017, we had 61 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 28 Perfect Scorers worldwide on the AMC 10A: Austen M., and two of our students were among the 65 Perfect Scorers worldwide on the AMC 10B: Ashwin A. and Brad Z. Remarkably, eight middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Very impressively, Bryan Z., a 6th grader, gained a score of 132 out of 150 on the AMC 10B.Read more at: 2017 AIME Qualifiers Announced — 61 Students Qualified for the AIME

In 2016, we had 36 students who are qualified to take AIME either through AMC 10A/12A or AMC 10B/12B. One of our students was among the 23 Perfect Scorers worldwide on the AMC 10A: Joel (Junyao) T. Particularly, seven middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Pravalika P., a 6th grader, got a 115.5 out of 150 on the AMC10B, which is very impressive. Read more at: 2016 AIME Qualifiers Announced — 36 Students Qualified for AIME

2011 – 2015: In total, 37 students scored above 120 on the American Mathematics Contest 10 (AMC 10) and qualified for the American Invitational Mathematics Examination (AIME); 26 students scored above 100 on the American Mathematics Contest 12 (AMC 12) and qualified for the American Invitational Mathematics Examination (AIME); 3 students qualified for the USA Mathematical Olympiad (USAMO), the highest level of math competition for high school students in the USA

2011 – 2015: In total, 23 students achieved perfect scores of 28 on the AMC 8

Read more at: Notable Achievements of Our Students

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Our Uniqueness

We have a long history of close collaboration with the MAA’s American Mathematics Competitions (AMC), which are dedicated to strengthening the mathematical capabilities of our nation’s youth, and are the first of a series of competitions in high school mathematics that determine the United States team for the International Mathematical Olympiad (IMO).

We are only one in the Washington DC metropolitan area to offer elementary, middle, and high-school level competition math courses. Our students have received top scores and awards at prestigious national and math competitions.

Great Benefits of Math Competitions

In an increasingly competitive college application pool, the process of mastering math skills through our courses and participating in the American Math Competitions will help students strengthen and diversify their extracurricular activities. These contests can motivate students’ interest and passion in math, and they can discover their talent through solving challenging problems different from those in the school classes. Many top colleges also request AMC scores as part of the college application process. Both MIT and Caltech have entry blanks on their official admission application forms for the applicant to enter their best AMC and AIME scores. Ivy League Colleges and Stanford ask for to the AMC and AIME scores in their Supplement to the Common Application Forms. Your children deserve the chance to list these scores on their applications! Good AMC scores will greatly enhance admission opportunities for students to elite colleges.

Read more at::

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Click HERE to find out more about SAT Prep!

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Over-Reliance on Calculators: A Heavy Burden on Fundamental Education

Posted on 2024-03-12 | Leave a comment

copyright-small Henry Wan, Ph.D.

The widespread use of calculators has introduced significant challenges to mathematics education. In primary and middle schools, excessive dependence on these devices is eroding students’ foundational mathematical abilities.

Mathematics education is not merely about performing calculations — it is about cultivating logical thinking and problem-solving skills. When students become accustomed to obtaining answers by simply pressing buttons, they lose the valuable process of reasoning through problems. A simple arithmetic operation, when solved mentally, requires an understanding of the order of operations, carrying and borrowing rules, and number relationships. These seemingly basic processes are, in fact, the cornerstone of mathematical thinking and cognitive development.

The Consequences of Over-Reliance on Calculators

Excessive use of calculators leads to a decline in students’ mathematical abilities. Research shows that students who rely heavily on calculators tend to have significantly weaker mental calculation skills than their peers who use them sparingly. This weakness is not just in calculation speed but also in number sense and conceptual understanding. When students lose their intuition for numbers, they struggle to solve complex mathematical problems that require deeper reasoning.

The premature introduction of calculators in primary and middle school creates a dependency that can be difficult to break. What begins as a reliance on calculators for basic arithmetic gradually turns into an inability to perform even the simplest calculations without them. Many students lose confidence in their ability to compute manually, feeling the need to verify even basic sums with a calculator. In extreme cases, this over-reliance cripples their fundamental calculation skills, leaving them unable to perform mental or written arithmetic efficiently.

A Phased Approach to Calculator Use

To address this issue, we advocate for a phased approach to calculator use in education:

  • Primary school students should be completely prohibited from using calculators to ensure they develop a solid foundation in arithmetic.
  • Middle school students may use calculators moderately under strict limitations, ensuring that they do not become over-reliant.
  • High school students can be allowed unrestricted use of calculators, as they transition to more advanced mathematical concepts that involve real-world applications.

During the critical years of mathematical development, students should be guided to establish a strong foundation through mental and written calculations. Developing mental arithmetic skills is not just about improving speed; it is about enhancing logical thinking and problem-solving ability. Primary school should be the stage where students solidify their number sense, while middle school should focus on further strengthening these skills before gradually introducing calculators in a controlled manner.

The Impact of Banning Calculators in Math Competitions

As is well known, prior to 2008, the American Mathematics Competitions (AMC) allowed students to use calculators. However, after our persistent appeals and protests, the Mathematical Association of America (MAA) implemented a landmark policy change prohibiting calculator use in AMC starting in 2008. This decision forced students to develop stronger mental and rapid calculation skills, significantly improving their overall mathematical abilities.

The ban was based on the realization that calculators were hindering the development of fundamental arithmetic skills. By removing this crutch, students were compelled to engage more deeply with numerical concepts, developing stronger intuition for numbers and a deeper understanding of mathematical principles. As a result, students not only became more proficient in calculations but also sharpened their problem-solving and logical reasoning skills — essential abilities for success in mathematics and beyond.

Training Students for Mental and Quick Calculation

To support this transition and further enhance students’ mathematical skills, we have introduced specialized training programs. Every summer, we offer intensive courses designed to help students improve their mental and rapid calculation abilities. More details can be found at Online Intensive Mental Math Course (Summer Session). These programs provide a structured environment where students refine their skills through a series of progressive exercises and challenges.

The impact of these initiatives has been profound. Students who participate in our summer programs consistently demonstrate remarkable improvements in their mathematical performance. They develop a greater appreciation for the beauty and logic of mathematics and gain the confidence to tackle complex problems without relying on calculators. By fostering a generation of students proficient in mental calculations, we are not only boosting their academic achievements but also preparing them for future success in fields that demand strong analytical and quantitative skills.

Conclusion

Mathematics education is fundamentally about nurturing thinking skills, and over-reliance on calculators is a major obstacle to achieving this goal. The prohibition of calculators in math competitions, along with structured training programs, has played a pivotal role in enhancing students’ mathematical abilities. These efforts reaffirm our commitment to building a generation of mathematically proficient individuals, equipped to excel in an increasingly competitive and data-driven world.

By reducing dependence on calculators and reinforcing mental arithmetic, we can ensure that students develop deep mathematical intuition, problem-solving abilities, and logical reasoning skills — qualities that will benefit them not only in academics but throughout their lives. Let us safeguard the integrity of basic education and lay a strong mathematical foundation for future generations.

 maausasf

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The Golden Rule of Learning Mathematics: Transitioning from Memorization to Deep Understanding and Creative Thinking

Posted on 2024-03-06 | Leave a comment

copyright-small Henry Wan, Ph.D.

The true key to mastering mathematics lies in transforming knowledge from something external — merely memorized — into an internalized skillset that becomes second nature. To achieve this, students must go beyond rote learning and actively engage in a process of deep comprehension and creative exploration.

Step 1: Recall — Testing Your Understanding

After attending a math class, immediately review the concepts covered without referring to any materials. Try to recall the key points discussed by the teacher, including formulas, theorems, and their derivations. The ability to reconstruct this information from memory is the best test of how effectively you absorbed the material during class. If you struggle to recall certain details, it signals areas that require further review.

Step 2: Derivation — Reinforcing Knowledge Through Independent Thought

Take out a notebook and write down the important formulas and theorems from memory. However, do not stop at simply writing them down — challenge yourself to re-derive the formulas and prove the theorems using your own thought process. This independent thinking exercise helps pinpoint gaps in your understanding and solidifies your grasp of mathematical principles. The process of struggling through a derivation on your own is invaluable, as it forces you to connect different pieces of knowledge logically rather than just memorizing results.

Step 3: Comparison — Evaluating and Refining Methods

After completing your derivations, open your textbook and class notes to compare your approach with those presented in the materials or by the teacher. This comparison often leads to valuable insights: perhaps your method is more intuitive, or maybe the textbook’s approach is more elegant and universally applicable. By analyzing the strengths and weaknesses of different methods, you develop a more profound and flexible understanding of mathematical concepts.

Step 4: Generalization — Expanding Mathematical Thinking

True mastery of mathematics extends far beyond simply deriving formulas, proving theorems, or solving problems. It involves questioning assumptions, identifying patterns, and generalizing principles to uncover deeper insights. Consider the Pythagorean Theorem as an example. Memorizing, deriving, proving, and applying the Pythagorean formula for right triangles is just the starting point. To truly grasp its significance, challenge yourself with these thought-provoking questions:

  • Why does the theorem specifically apply to right triangles?
  • How does the relationship change if the triangle is acute? (Hint: The equation transforms into an inequality.)
  • How does the relationship change if the triangle is obtuse? (Hint: The equation also transforms into an inequality.)
  • How does the theorem evolve when extended from two dimensions to three, four, or eve n-dimensional space?
  • What happens when we move from Euclidean space to spherical geometry? (On a sphere, the classical Pythagorean Theorem no longer holds, and an entirely new geometric relationship emerges.)

By exploring these deeper questions, you shift from merely using mathematical tools to truly understanding their foundations, limitations, and broader implications. This approach nurtures creativity, critical thinking, innovation, and problem-solving skills — hallmarks of true mathematical mastery.

A Real Example: From Competitive Math to Cutting-Edge Research

One of our students, inspired by this approach, successfully extended the Pythagorean theorem and the Law of Cosines to higher-dimensional spaces and eventually to spherical geometry. Under our guidance, the student refined this work into a rigorous mathematical paper, which we helped recommend for publication in a prestigious journal of the Mathematical Association of America. This outstanding academic achievement became a key stepping stone, ultimately securing the student’s admission to MIT.

Why This Method Works: From Passive Learning to Active Discovery

This structured learning approach — Recall, Derivation, Comparison, and Generalization — transforms passive reception into active engagement. Rather than simply memorizing formulas, you develop a deep contextual understanding and an independent problem-solving mindset. These habits not only enhance academic performance but also cultivate the ability to think critically, explore new ideas, and innovate — skills that extend far beyond the classroom.

Mathematics is not just about solving problems — it’s about discovering patterns, questioning assumptions, and pushing the boundaries of what you know. By following this learning strategy, you will not only excel in math but also develop a lifelong ability to think deeply and creatively.

 maausasf

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The Learning Trifecta: Preview, Note-taking, and Review

Posted on 2024-03-05 | Leave a comment

copyright-small Henry Wan, Ph.D.

Learning effectively requires a structured approach. A good study habit includes three essential steps: previewing before class, taking notes during class, and reviewing after class. These are three interconnected and essential steps in the learning process, forming a complete learning cycle. When executed effectively, can significantly enhance your understanding and retention of knowledge.

Previewing Before Class

Before attending a class, students should take time to go through the relevant materials. Previewing helps them get a basic understanding of the topic, identify key points, and formulate any questions they may have.. This preparation not only makes it easier to follow the teacher’s explanations but also enables students to engage more actively in class discussions and absorb new knowledge more effectively.

Taking Notes During Class

During the lesson, taking clear and organized notes is essential. This skill helps students stay focused and systematically organize information. Well-taken notes capture key concepts, important formulas, and explanations that may not be found in textbooks. Writing information in one’s own words enhances understanding and retention, making it easier to review later. Additionally, structured notes serve as a valuable resource for reinforcing learning and preparing for exams.

Reviewing After Class

After class, reviewing the material is crucial for reinforcing what has been learned. Students should go through their notes, clarify any unclear points, and consolidate their knowledge by recalling key concepts and main ideas without referring to their materials. Regular review helps prevent forgetting and promotes a deeper understanding of the subject. Additionally, completing homework assignments and engaging in discussions with classmates can further strengthen their grasp of the material.

Conclusion

These three steps are interconnected and essential for effective learning. Previewing lays the groundwork for understanding new material, note-taking captures key points during the lesson, and reviewing reinforces and solidifies knowledge. By consistently following this cycle, students can enhance their comprehension, retain information more effectively, and improve their academic performance.

Developing this habit not only leads to greater academic success but also cultivates a lifelong ability to learn efficiently. Remember, learning is a continuous journey, not just a destination. By embracing this structured approach and integrating it into your study routine, you can unlock your full potential and achieve your academic goals.

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How To Use A Solutions Manual Correctly?

Posted on 2024-03-05 | Leave a comment

copyright-small Henry Wan, Ph.D.

We have meticulously developed the Solutions Manual to provide detailed, step-by-step solutions for all homework problems. Each problem includes at least one solution, all of which were derived without the use of a calculator to encourage students for developing mathematical reasoning, problem-solving abilities, and creative thinking skills.

In cases where multiple solutions are presented, they are included to highlight key contrasts in problem-solving approaches. These alternative methods help students develop a deeper understanding of mathematical concepts by exploring different perspectives, such as:

  • Algebraic vs. Geometric — Solving problems through symbolic manipulation versus visual or spatial reasoning.
  • Elementary vs. Advanced — Approaching problems using fundamental techniques versus more sophisticated methods.
  • Computational vs. Conceptual — Focusing on numerical calculations versus underlying theoretical principles.
  • Explicit vs. Implicit — Directly solving for unknowns versus deriving solutions through indirect reasoning.
  • Analytic vs. Discrete — Using continuous methods versus discrete, step-by-step reasoning.
  • Forward-Solving vs. Back-Solving — Progressing logically from given information versus working backward from the desired outcome.

Understanding these different approaches helps students become more flexible and adaptable problem solvers, equipping them with the skills necessary for success in mathematical competitions and beyond.

To ensure students use the Solutions Manual as a tool for learning rather than a shortcut to answers, we have written this article, “How to Use a Solutions Manual Correctly?” This guide provides strategies to maximize the manual’s benefits while reinforcing independent problem-solving skills, ultimately fostering deeper comprehension and mathematical growth.

Many of the problems you encounter are subtle or complex, requiring careful thought — and time! — before a clear solution method emerges. The best way to learn is by attempting to solve a problem on your own, even if you don’t succeed at first. This process of grappling with challenges is crucial for deepening your understanding.

Learning mathematics requires a certain amount of “healthy frustration,” which is a natural part of developing problem-solving skills. You may need to try different approaches (some of which may lead nowhere or a dead end) until you find a viable solution. While this process can be time-consuming, it is important to persist without immediately relying on outside help. If you turn to the solutions manual too quickly, you risk missing out on the critical thinking and problem-solving skills that are key to success, particularly in competitive settings like math contests. Simply understanding the solutions provided in the manual does not mean you’ve truly mastered the material!

The solutions manual can be a helpful learning tool if used correctly, but it can also subtly hinder your progress if relied upon too heavily. How you use the manual can significantly affect your learning experience. If you use it prematurely or excessively, you may end up undermining your own efforts to master the material and perform well on contests.

The most important principle to remember is this: Do not consult the solutions manual until you have made a genuine attempt to solve the problem yourself. Ideally, you should use the manual primarily to confirm your answer. In many cases, your solution will align with the one in the manual, but occasionally, you may discover a different approach that is equally correct — or even more efficient — than the one presented. If you find an alternative method, we would love to hear about it! Please send us your solution at mathteam@ivyleaguecenter.org.

If, after a substantial effort, you still can’t find the solution, then it’s appropriate to look at solution offered in the manual. Even then, start by reading only the beginning of the solution to see if you can continue on your own. The goal is not just to arrive at the answer but to fully engage with the process, which will ultimately deepen your understanding and develop your problem-solving.

The goal is not just to reach the answer but to immerse yourself in the process, enhancing your understanding, sharpening your problem-solving skills, and fostering your creative thinking.

The goal is not just to reach the answer but to immerse yourself in the process, enhancing your understanding, sharpening your problem-solving skills, and fostering your creative thinking.

By using the solutions manual in the right way, you will maximize your learning and enhance your ability to solve problems independently — skills that are invaluable in both academic settings and math competitions.

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Why Drawing a Good Diagram Is Important to Solve a Geometry Problem?

Posted on 2024-03-01 | Leave a comment

copyright-small Henry Wan, Ph.D.

Geometry is a branch of mathematics that heavily relies on visualization. Unlike algebra, where equations and numbers dominate problem-solving, geometry problems often involve shapes, angles, measurements, and spatial relationships. One of the most effective tools for tackling geometry problems is a well-drawn diagram. A clear, accurate diagram not only helps in understanding the given information but also reveals hidden relationships that might not be immediately obvious. Below are several reasons why drawing a good diagram is essential when solving geometry problems.

  1. Enhances Understanding of the Problem

A geometry problem often involves complex relationships between points, lines, angles, and shapes. Without a visual representation, these relationships can be difficult to grasp. Drawing a diagram translates abstract descriptions into concrete images, making it easier to grasp the given information and see how different elements interact. By sketching the diagram, you can identify key points, label known values, and ensure that you correctly interpret the problem statement. This step is especially useful for word problems that describe geometric figures verbally rather than presenting them visually.

  1. Helps Identify Important Geometric Properties

When solving a geometry problem, identifying key values and conditions is essential for finding the solution. Drawing a diagram allows one to clearly label known angles, lengths, and relationships such as parallel lines, perpendicular bisectors, or congruent triangles. This visual representation helps organize information systematically, reducing the risk of overlooking important details. More importantly, a well-drawn diagram highlights crucial geometric properties such as symmetry, parallelism, congruence, and similarity, which often hold the key to an efficient solution. For example, a carefully constructed diagram might reveal that two triangles are similar, enabling the straightforward application of proportional reasoning.

  1. Reduces Errors and Misinterpretations

Without a diagram, it is easy to misread a problem or overlook critical details, increasing the risk of misinterpreting given information or making calculation errors. A well-drawn diagram serves as a visual checkpoint, helping problem-solvers verify their steps and ensure their reasoning aligns with the actual figure. Incorrect assumptions can often be identified quickly by reviewing a clearly labeled diagram. Additionally, a diagram ensures that angles, side lengths, and relationships are accurately represented, minimizing the chances of computational or logical errors.

  1. Facilitates the Application of Theorems and Formulas

Many geometric theorems, such as the Pythagorean Theorem, the Angle Bisector Theorem, the properties of similar triangles, the properties of circles, or the sum of interior angles in a polygon, become easier to apply when visualized in a diagram. A well-drawn figure highlights key elements like right angles, perpendicular bisectors, and tangent lines, guiding the solver to the correct approach.

  1. Encourages Logical Thinking and Pattern Recognition

A diagram allows problem-solvers to explore different approaches and recognize patterns that may not be immediately apparent from the text alone. For example, extending a line, drawing an auxiliary shape, or marking equal segments and congruent angles can reveal insights that simplify the problem. Many competition-level geometry problems become significantly easier with a well-placed additional construction.

Additionally, a lot of geometry problems require logical reasoning, and a diagram serves as a structured visual aid to support step-by-step analysis. It helps track the flow of arguments, ensuring that conclusions logically follow from the given premises.

  1. Saves Time in Problem Solving

In competitive math settings, time is a critical factor. A good diagram often leads to a quicker solution by allowing direct visualization of relationships rather than relying on lengthy calculations. Instead of writing out multiple equations, a simple observation in a well-drawn diagram might provide an instant shortcut to the answer.

How to Draw an Effective Diagram?

To maximize the benefits of a diagram, consider the following tips:

  • Use a ruler (if time allows) or draw neatly by hand. A clear, proportional diagram prevents misinterpretation.
  • Label key points, angles, and lengths. This helps keep track of known values and relationships.
  • Mark congruent or similar segments. Highlighting these properties can make important relationships stand out.
  • Add auxiliary lines if necessary. Sometimes, drawing an extra line, such as a perpendicular or a median, simplifies the problem significantly.
  • Avoid cluttering the diagram. Too many unnecessary details can lead to confusion rather than clarity.

Conclusion

Drawing a good diagram is a fundamental skill in solving geometry problems. It enhances understanding, organizes key information, reduces errors, reveals crucial properties, displays patterns, supports logical reasoning, and facilitates the application of theorems. Whether tackling a school assignment, preparing for math competitions, or solving complex geometric proofs, investing a few moments in creating an accurate and well-structured diagram can be the key to success. By developing strong diagram-drawing habits, students can approach geometry problems with confidence and efficiency.

maausasf

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2024 Special Spring Session – Competitive Math Courses

Posted on 2024-02-20 | 1 comment

Spring is the best time to develop students’ math skills and to prepare for the American Mathematics Competitions!

Only undertake what you can do in an excellence fashion. There are no prizes for average performance.

  • 2024 AMC 8: 10 perfect scorers. 54 students got the DHR. 29 students got the HR.
  • 2023 AMC/AIME: 99 AIME qualifiers. 1 AMC 10 perfect scorer. 1 AMC 12 perfect scorer.
  • 2023 JMO/AMO: 8 USAMO Awardees and 7 USAJMO Awardees
    • 1 USAMO Gold Award, 1 USAMO Silver Award, 4 USAMO Bronze Awards, and 2 USAMO Honorable Mention Awards.
    • 1 USAJMO Top Winner, 1 USAJMO Winner, and 5 USAJMO Honorable Mention Awards.
  • 2023 MOP: 4 MOP winners.

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Competitive Math Program — 2004 Special Spring Session Schedule

Class Day/Time Grade
Online Intensive AMC 8/Mathcounts Prep Special Spring Session: Circle Geometry and Advanced Topics

10 Weekends (EASTERN Time: 6:00 – 8:00 pm), Total: 22 Hours
3/30,  4/6,  4/13,  4/20,  4/27,  5/4,  5/11,  5/18,  5/25,  6/1

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 4-8
Online Intensive AMC 10/12/ARML Prep Special Spring Session: Circles and Advanced Geometry

9 Weekends (EASTERN Time: 6:00 – 8:00 pm), Total: 18 Hours

4/14,  4/21,  4/28,  5/5,  5/12,  5/19, 5/26, 6/2,  6/9 (Final Mock Exam/Review)

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 6-11
Online Intensive AIME Prep Special Spring Session:  Advanced Algebra

9 Classes  (EASTERN Time: 3:00 – 4:30 pm), Total: 13.5 Hours

4/14,  4/21,  4/28,  5/5,  5/12,  5/19, 5/26, 6/2,  6/9 (Final Mock Exam/Review)

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 6-12

We record all of our lessons as a big bonus so that our students can watch class videos after class for review and self-study.

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There are many math competitions in the United States. Of those, only

AMC → AIME → USAMO sequence

would take you to the IMO (International Math Olympiad), the highest level math competition for high school students in the world!

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Featured Math Instructors

All of our sessions are taught by highly qualified instructors who are excellent experts on preparing students for the exam. We distinguish ourselves by the high quality of our instructors. Finding top-quality instructors is no easy task. We’ve hand-picked some of the best, including graduates of Ivy League institutions.

Our instructors are dedicated to teaching and student success. They are very knowledgeable, patient, available, and willing to help our students. Our students receive a quality education that goes beyond the classroom.

Meet some of them here:

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Our Students

In 2023, we had 8 students who won USAMO awards and 7 students who won USAJMO awards.

  • 1 USAMO Gold Award, 1 USAMO Silver Award, 4 USAMO Bronze Awards, and 2 USAMO Honorable Mention Awards.
  • 1 USAJMO Top Winner, 1 USAJMO Winner, and 5 USAJMO Honorable Mention Awards.

Read more at: 2023 USAMO and USAJMO Awardees Announced — Congratulations to Eight USAMO Awardees and Seven USAJMO Awardees

In 2023, we had 90 students who obtained top scores on the AMC 8 contest!

  • 8 of our students were among the top 81 worldwide winners (Perfect Scorers).
  • 51 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers. They were among the 697 worldwide winners.
  • 31 students received National Honor Roll Certificates awarded to top 5% test takers. They were among the 2,571 worldwide winners.
  • 90 out of our 93 students (96.8%) received National Awards for the AMC 8 from the Mathematical Association of America.

Read more at: 2023 AMC 8 Results Just Announced — Eight Students Received Perfect Scores

In 2022, we had 96 students who qualified for the AIME either through the AMC 10A/12A or the AMC 10B/12B. One of our students was among the 6 Perfect Scorers worldwide on the AMC 10A: Justin W. and one of our students was among the 3 Perfect Scorers worldwide on the AMC 12B: Ming Y. Read more at: 96 Students Qualified for the 2023 AIME and 2 Students Received Perfect Scores on the 2023 Fall AMC 10/12

In 2022, we had 3 students qualified for the Math Olympiad Summer Program. Read more at: Brendon J., Kyle S., and Isabella Z. Qualified for the 2022 Math Olympiad Summer Program

In 2022, we had 1 student Competes in International Girls’ Math Olympiad. Read more at: sabella Z. Competes in International Girls’ Math Olympiad

In 2022, we had 7 students qualified for the USAMO and 7 students for the USAJMO. Read more at: 2022 USAMO and USAJMO Qualifiers Announced — Seven Students Qualified for the USAMO and Seven Students for the USAJMO.

In 2022, we had 88 students who obtained top scores on the AMC 8 contest!

  • 10 of our students were among the top 131 worldwide winners (Perfect Scorers), as shown in Table 1. Click Here see a full list of the 131 worldwide winners.
  • 52 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers. They were among the 1,010 worldwide winners. Click HERE see a full list.
  • 26 students received National Honor Roll Certificates awarded to top 5% test takers. They were among the 2,449 worldwide winners. Click HERE see a full list.
  • 88 out of our 91 students (96.7%)received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2022 AMC 8 Results Just Announced — Ten Students Received Perfect Scores

In Fall 2021, we had 93 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 5 Perfect Scorers worldwide on the AMC 10A: Nina L. and one of our students was among the 2 Perfect Scorers worldwide on the AMC 10B: Ming Y. Read more at: 93 Students Qualified for the 2021 Fall AIME and 2 Students Received Perfect Scores on the 2021 Fall AMC 10/12

In 2021, we had 6 students qualified for the USAMO and 6 students for the USAJMO. Read more at: 2021 USAMO and USAJMO Qualifiers Announced — Six Students Qualified for the USAMO and Six Students for the USAJMO

In Spring 2021, we had 91 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students was among the 17 Perfect Scorers worldwide on the AMC 12A: Evan L. and Suraj O. and one of our students was among the 27 Perfect Scorers worldwide on the AMC 10A: Xinchen L. Read more at: 91 Students Qualified for the 2021 AIME and 3 Students Received Perfect Scores on the 2021 AMC 10/12

In 2021, we had 8 students who got into the MathCounts state-level top 10. Yunyi L. won 9th Place in the 2021 MathCounts National Competition!

In 2020, we had 79 students who obtained top scores on the AMC 8 contest!

  • 5 of our students were among the top 57 worldwide winners (Perfect Scorers).
  • 49 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 25 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 79 out of our 81 students (97.5%) received National Awards for the AMC 8 from the Mathematical Association of America.

Read more at: 2020 AMC 8 Results Just Announced — Five Students Received Perfect Scores

In 2020, we had 2 students, Isabella Z. and Sameer P., who were among the 61 students selected nationwide to attend. Read more at: Warmest congratulations to Isabella Z. and Sameer P. for being accepted into the Math Olympiad Program!

In 2020, we had 82 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 11 Perfect Scorers worldwide on the AMC 12A: Yiyang X, and one of our students was among the 13 Perfect Scorers worldwide on the AMC 10A: Jason W.. 43 middle schoolers and 9 elementary schoolers qualified for the AIME!

Read more at: 2020 AIME Qualifiers Announced — 82 Students Qualified for the AIME

In 2019, we had 71 students who obtained top scores on the AMC 8 contest!

  • 8 of our students were among the top 151 National Winners (Perfect Scorers), including 2 sixth graders.
  • 36 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers, as shown in Table 2.
  • 27 students received National Honor Roll Certificates awarded to top 5% test takers, as shown in Table 3.
  • 71 out of our 73 students (97.3%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2019 AMC 8 Results Just Announced — Eight Students Received Perfect Scores

In 2019, we had 4 students qualified for the USAMO and 4 Students for the USAJMO.

  • Of the 280 USA Math Olympiad national qualifiers, 4 are our students: Luke C., Zipeng L., Sameer P., and Peter P.
  • Of the 235 USA Junior Math Olympiad national qualifiers, 4 are our students: Michael H., Noah W., Holden W., and Isabella Z.

Read more at: 2019 USAMO and USAJMO Qualifiers Announced — Four Students Qualified for the USAMO and Four Students for the USAJMO

In 2019, we had 76 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 22 Perfect Scorers worldwide on the AMC 10A: Noah W.and one of our students were among the 10 Perfect Scorers worldwide on the AMC 12B: Kenneth W. Very impressively, 32 middle schoolers and 7 elementary schoolers qualified for the AIME!

Read more at: 2019 AIME Qualifiers Announced — 76 Students Qualified for the AIME

In 2018, we had 64 students who obtained top scores on the AMC 8 contest!

  • 3 of our students were among the top 44 National Winners (Perfect Scorers): Eric B., Kevin Y., and Isabella Z.
  • 40 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 21 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 64 out of our 66 students (96.5%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2018 AMC 8 Results Just Announced — Three Students Received Perfect Scores

In 2018, we had 73 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students were among the 35 Perfect Scorers worldwide on the AMC 10A: Austen M. and Jason W.  and two of our students were among the 21 Perfect Scorers worldwide on the AMC 12B: Kaan D. and Edward W. Remarkably, 11 middle schoolers and 2 elementary schoolers qualified for the AIME!

Read more at: 2018 AIME Qualifiers Announced — 73 Students Qualified for the AIME

In 2017, we had 63 students who earned top scores on the AMC 8 contest!

  • 7 of our students were among the top 75 National Winners (Perfect Scorers).
  • 34 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 22 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 63 out of our 65 students (97%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2017 AMC 8 Results Just Announced — Seven Students Received Perfect Scores

In 2017, we had 61 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 28 Perfect Scorers worldwide on the AMC 10A: Austen M., and two of our students were among the 65 Perfect Scorers worldwide on the AMC 10B: Ashwin A. and Brad Z. Remarkably, eight middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Very impressively, Bryan Z., a 6th grader, gained a score of 132 out of 150 on the AMC 10B.

Read more at: 2017 AIME Qualifiers Announced — 61 Students Qualified for the AIME

In 2016, we had 36 students who are qualified to take AIME either through AMC 10A/12A or AMC 10B/12B. One of our students was among the 23 Perfect Scorers worldwide on the AMC 10A: Joel (Junyao) T. Particularly, seven middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Pravalika P., a 6th grader, got a 115.5 out of 150 on the AMC10B, which is very impressive.

Read more at: 2016 AIME Qualifiers Announced — 36 Students Qualified for AIME

2011 – 2015: In total, 37 students scored above 120 on the American Mathematics Contest 10 (AMC 10) and qualified for the American Invitational Mathematics Examination (AIME); 26 students scored above 100 on the American Mathematics Contest 12 (AMC 12) and qualified for the American Invitational Mathematics Examination (AIME); 3 students qualified for the USA Mathematical Olympiad (USAMO), the highest level of math competition for high school students in the USA

2011 – 2015: In total, 23 students achieved perfect scores of 28 on the AMC 8

Read more at: Notable Achievements of Our Students

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Our Uniqueness

We have a long history of close collaboration with the MAA‘s American Mathematics Competitions (AMC), which are dedicated to strengthening the mathematical capabilities of our nation’s youth, and are the first of a series of competitions in high school mathematics that determine the United States team for the International Mathematical Olympiad (IMO).

We are only one in the Washington DC metropolitan area to offer elementary, middle, and high-school level competition math courses. Our students have received top scores and awards at prestigious national math competitions.

Great Benefits of Math Competitions

In an increasingly competitive college application pool, the process of mastering math skills through our courses and participating in the American Math Competitions will help students strengthen and diversify their extracurricular activities. These contests can motivate students’ interest and passion in math, and they can discover their talent through solving challenging problems different from those in the school classes. Many top colleges also request AMC scores as part of the college application process. Both MIT and Caltech have entry blanks on their official admission application forms for the applicant to enter their best AMC and AIME scores. Ivy League Colleges, Caltech, and Stanford ask for to the AMC and AIME scores in their Supplement to the Common Application Forms. Your children deserve the chance to list these scores on their applications! Good AMC scores will greatly enhance admission opportunities for students to elite colleges.

Read more:

Contact Information:

Ivy League Education Center
Tel:  240-300-4380     or     240-406-3402（中文专线）
Email:  chiefmathtutor@gmail.com

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2024 AMC 8 Results Just Announced — Ten Students Received Perfect Scores

Posted on 2024-02-19 | Leave a comment

HEARTFELT CONGRATULATIONS TO THE STUDENTS WHO EARNED TOP SCORES ON THE 2024 AMC 8 CONTEST!

  • 10 of our students were among the top 116 worldwide winners (Perfect Scorers).
  • 54 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers. They were among the 697 worldwide winners. 
  • 29 students received National Honor Roll Certificates awarded to top 5% test takers. They were among the 2,683 worldwide winners. 
  • 93 out of our 96 students (96.9%) received National Awards for the AMC 8 from the Mathematical Association of America

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The 2024 AMC 8 (American Mathematics Competitions 8) was held on January 18, 2024 through January 24, 2024. The AMC 8 is the most rigorous nationwide mathematics competition at the middle school level, dedicated to the goal of strengthening the mathematical capabilities of our nation’s youth. The AMC 8 has a total score of 25. Ten of our students were among the 116 Worldwide Winners (Perfect Scorers).

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In 2024, there were 96 students in grades 4-8 who attended our AMC 8 Prep, AMC 10/12 Prep, and AIME Prep Classes, including One-on-One Private Coaching and Small Group (4-10 students) Classes. All of them attended the AMC 8 contest on January 18, 2024 through January 24, 2024, and their average score is 20.6. Particularly, 93 students received National Awards for the AMC 8 from the Mathematical Association of America. Furthermore, 37 students in grade 6 or under received National Awards.

All our students who achieved the top scores on the AMC 8 actually attended our high level AMC 10/12/AIME classes, not our standard level AMC 8 classes. They know that in order to get a top score, they must aim even higher!shoot-for-the-mooneven-if-you-missyoull-land-among-the-stars-inspirational-quote

There was a total of 272,0359 students worldwide participated in the 2024 AMC 8 contest from over 2,000 schools. In the USA, 231,478 students participated, and the overall national average score is 10.54 out of a maximum of 25. All our students achieved an average score of 22.8 that is much higher than the overall national average score.

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Top scorers and statistics can be found at http://amc-reg.maa.org/reports/generalreports.aspx

Read more at:

Click HERE find out more about Math Competitions!

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2024 AMC 8 Honor Roll and Honor Roll of Distinction Cut-off Scores

Posted on 2024-02-19 | Leave a comment

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  • Honor Roll of Distinction (Top 1%): Score of 22
  • Honor Roll of Certificate (Top 5%): Score of 18
  • Achievement Honor Roll (6th Grade and below): Score of 15.

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This year’s contest is of intermediate difficulty compared to the contests in the last 5 years. For more details, please see:

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Read more at:

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Click HERE find out more about Math Competitions!sat-logo-3

Click HERE to find out more about SAT Prep!

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